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\mainmatter              % start of the contributions
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\title{A Possibilistic Valid-time Model}
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%\titlerunning{A Fuzzy Valid-Time Model}  % abbreviated title (for running head)
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\author{Jos\'e Enrique Pons\inst{1} \and Christophe Billiet\inst{2} \and Olga Pons Capote\inst{1} \and Guy De Tr\'e\inst{2}}
%Jeffrey Dean \and David Grove \and Craig Chambers \and Kim~B.~Bruce \and
%Elsa Bertino}
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\authorrunning{Jos\'e Enrique Pons et al.} % abbreviated author list (for running head)
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%%%% list of authors for the TOC (use if author list has to be modified)
%\tocauthor{Ivar Ekeland, Roger Temam, Jeffrey Dean, David Grove,
%Craig Chambers, Kim B. Bruce, and Elisa Bertino}
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\institute{
Department of Computer Science and Artificial Intelligence, Universidad de Granada, Escuela T\'ecnica Superior de Ingenier\'ia Inform\'atica \\
C/Periodista Daniel Saucedo Aranda s/n, E-18071, Granada, Spain\\
\email{jpons,opc@decsai.ugr.es}\\ 
%WWW home page:
%\texttt{http://users/\homedir iekeland/web/welcome.html}
%\and
%Universit\'{e} de Paris-Sud,
%Laboratoire d'Analyse Num\'{e}rique, B\^{a}timent 425,\\
%F-91405 Orsay Cedex, France
\and 
Department of Telecommunications and Information Processing, Ghent University \\
Sint-Pietersnieuwstraat 41 B-9000, Ghent, Belgium.
\email{Christophe.Billiet,Guy.De.Tre@ugent.be}
}

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\begin{abstract}
Information in databases can be imperfect and this imperfection has several forms and causes. In some cases, a single value should be stored, but it is (partially) unknown. The uncertainty about which value to store leads to the aforementioned imperfection. In temporal databases, uncertainty can arise, concerning which temporal notion needs to be stored. Because in temporal databases, temporal notions influence the consistency with which the database models the reality, this uncertainty has a direct impact on the consistency of the model. To represent this temporal uncertainty, previous works have adapted fuzzy sets with conjunctive interpretation, an approach that might prove misleading. This work presents a model that represents the uncertainty using possibility and necessity measures, which are fuzzy sets with disjunctive interpretations.
\end{abstract}

\begin{keywords}
temporal databases, fuzzy databases, information systems, incompleteness
\end{keywords}

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\section{Introduction}
\label{sec:Introduction}
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\section{Preliminaries}
\label{sec:preliminaries}
\input{preliminaries}



\section{Proposal}
\label{sec:proposal}
\input{proposal}


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% FURTHER RESEARCH WORK
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\section{Conclusions and Further Research}
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\section*{Acknowledgements}
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Part of the researchers are supported by the grant BES-2009-013805 in the project TIN2008-02066: \emph{Fuzzy Temporal Information treatment in RDBMS}.


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